Decomposition tables for experiments. II. Two--one randomizations

Details Decomposition tables for experiments. II. Two--one randomizations Decomposition tables for experiments. II. Two--one randomizations

2010-11-11

arxiv.org/abs/1011.2653v1

Annals of Statistics 2010, Vol. 38, No. 5, 3164-3190

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS785 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/09-AOS785

We investigate structure for pairs of randomizations that do not follow each other in a chain. These are unrandomized-inclusive, independent, coincident or double randomizations. This involves taking several structures that satisfy particular relations and combining them to form the appropriate orthogonal decomposition of the data space for the experiment. We show how to establish the decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that competing designs can be evaluated. This leads to recommendations for when the different types of multiple randomization should be used.

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